Question: What is the period of the function $g(x)=2\cos(7x+5)+1$ ? Give an exact value. units
Solution: Period in sinusoids of the form $y=a\cos(bx+c)+d$ Graphically, the period of a sinusoidal function is the horizontal distance between the ends of a single cycle of its graph. The period of a sinusoid of the form $y={a}\cos( bx + c) + {d}$ is equal to $\dfrac{2\pi}{| b|}$. [How can we justify this given our graphical understanding of period?] Finding the period The period of $g(x) = 2\cos({7}x+5)+1$ is: $\begin{aligned} \text{period}&=\dfrac{2\pi}{|{b}|}\\\\ &=\dfrac{2\pi}{| 7|} \\\\\\\\\\ &= \dfrac{2\pi}{7} \\ \end{aligned}$ The answer The period of $g(x) = 2\cos({7}x+5)+1$ is $\dfrac{2\pi}{7}$ units.